Simple theory for the critical adsorption of a fluid

Isotherms for the adsorption of a fluid can be obtained from standard theories of fluids by regarding the surface as a single giant sphere dissolved in the fluid. The amount adsorbed is then an integral over the giant-spherefluid-molecule correlation function. Simple considerations show that the critical exponent for the adsorption isotherm is related to, the critical exponent for the compressibility. Using the mean-spherical approximation, it is argued that the adsorption-isotherm critical exponent is /2 if the surface-fluid interaction is sufficiently short-ranged. This result is in reasonable agreement with the recent experimental findings of Bl̈mel and Findenegg. © 1985 The American Physical Society.